POSITIVE SOLUTIONS OF PERTURBED ELLIPTIC PROBLEMS INVOLVING HARDY POTENTIAL AND CRITICAL SOBOLEV EXPONENT

In this paper, we are concerned with the following nonlinear Schrodinger equations with hardy potential and critical Sobolev exponent {-Delta u + lambda a(x)u(q) = mu/vertical bar x vertical bar(2) + vertical bar u vertical bar(2*) (-2)u, in R-N , u > 0, in D-1,D-2 (R-N), (1) where 2* = 2N/N-2 is the critical Sobolev exponent, 0 <= mu < mu = (N-2)(2)/4, a(x) is an element of C(R-N). We first use an abstract perturbation method in critical point theory to obtain the existence of positive solutions of ( I) for small value of Secondly, we focus on an anisotropic elliptic equation of the form -div(B-lambda(x)del u) + lambda a(x)u(q) = mu u/vertical bar x vertical bar(2) vertical bar u vertical bar(2)* (-2) u,x is an element of R-N. (2) The same abstract method is used to yield existence result of positive solutions of (2) for small value of vertical bar lambda vertical bar.